In this UK (at least), this is known as "card clash". You can't select which card is used. I'm not sure what the EMV contactless specification actually says, but anecdotally terminals will either fail to process the transaction (general card read error or a more specific collision message) or unpredictably select a card to charge.

Most card issuers (and companies like TfL - Transport for London, the transport authority who use contactless travel cards) recommend taking your card our of your wallet if you have more than one contactless card.